What the attack is measuring is basically the transmission delay to the device and back. The device (or the mobile network operator) doesn't know that delay, so they can't cancel it out. If you add a constant wait time you only accomplish something if the attacker doesn't know about that, otherwise they simply subtract that. And random variance just makes the measurement noisier, send enough SMS and the noise averages out.

If they have each delivery report randomly pick one of several ranges of potential delay (0-2seconds, 1-3, 2-4) and then pick a random amount within whichever range is selected, would it still be possible to average out the randomness to get an accurate location? Actually I'm not sure that's any better than just having one wide range that it picks randomly from, but it could expand that range for each message over the first 5 per hour or whatever to make it harder to spam enough to average out without getting to extremely delayed delivered notifications?